>>Yes - while each computation is an integer, the average is being computed by dividing the sum of the integer values by the count of the integer values in the group. You'll have to coerce the result into an integer for display purposes; this is most easily done by using a format with no decimal places. This will force the decimals to truncate rather than providing a correctly rounded integer value that more accurately reflects the mean, but it doesn't sound like that matters.
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>Additionally, if there's a need to sum them, then we should use report variables. A simple variable which would have a value of Int(average_field), Calculate=nothing, can be used throughout the report instead of the field itself, including the places where it should appear in totals.

Absolutely the case; using a report variable and then rounding the result could be done to get an accurately-rounded mean throughout the report.